No, that won't work.
The USB port on the OBi only works with the OBi WiFi dongle to attach the OBi as a network client, to your router, via WiFi. It can't attach downstream devices via WiFi. and you can't use it to attach a USB printer.
If the HP printer has an ethernet port, use it to connect to your home network, either at a router, switch, or the LAN port on the OBi (the Ethernet jack). If the HP printer has a WiFi port, use it to connect to your home network.
If the HP printer is so old or cheap that it doesn't have any network capability, then it's time to buy a new printer.